Exam 7: Applications of Integration

Use the disk or shell method to find the volume of the solid generated by revolving the region in the first quadrant bounded by the graph of the equation about the given line. (i) the x-axis; (ii) the y-axis

Neglecting air resistance and the weight of the propellant, determine the work done in propelling a four-ton satellite to a height of 400 miles above earth. Assume that Earth has a radius of 4000 miles.

A 22-foot chain that weighs 2 pounds per foot hangs from a winch 22 feet above ground level. Find the work done by the winch in winding up the entire chain. ​

Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. Round your answer to two decimal places.

Use the shell method to find the volume of the solid generated by revolving the plane region bounded by , about the line . ​

Use the disk or shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line .

Use the Theorem of Pappus to find the volume of the solid formed by revolving the region bounded by the graphs of about the x-axis. Round your answer to two decimal places.

Find for the lamina of uniform density bounded by the graphs of the equations and .

Find the center of mass of the point masses lying on the x-axis.

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines.

Set up and evaluate the definite integral for the area of the surface formed by revolving the graph of about the y-axis. Round your answer to three decimal places.

Find the area of the surface generated by revolving the curve about the y-axis. .

Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by and about the -axis.

Find the arc length of the graph of the function over the interval .

Find for the lamina of uniform density bounded by the graphs of the equations . ​

A quantity of gas with an initial volume of 5 cubic feet and a pressure of 1700 pounds per square foot expands to a volume of 9 cubic feet. Find the work done by the gas for the given volume and pressure. Round your answer to two decimal places. Assume the temperature of the gas in this process remain constant.

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line .

The vertical cross section of an irrigation canal is modeled by , where x is measured in feet and corresponds to the center of the canal. Use the integration capabilities of a graphing utility to approximate the fluid force against a vertical gate used to stop the flow of water if the water is feet deep. Round your answer to three decimal places.

Find the fluid force of a square vertical plate submerged in water, where meters and the weight-density of water is 9800 newtons per cubic meter.

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis.